Firstly, go to your character-specific forum and read the guides.
You’ll want to be learning normals, bread-n-butter combos, mix-ups, and specific matchups. You should be learning what normals to use for pressuring, poking, and anti-air. Maybe you can practice by only using normals on the CPU to get a good grasp on them. I can beat the CPU with just normals. After that, move on to special moves and learn how to use them effectively. Also try to learn the appropriate times to throw or use focus attacks on the CPU.
Once you got those things down, learn some basic/easy combos and cross-up combos. Learn to execute them precisely and not by simply mashing and hoping they’ll come out. There ARE situations when mashing can be a good thing though, but don’t rely on it for general execution.
Next, learn and work on your execution with bread-n-butter combos. Practice this in training mode. It’s important to maximize your damage when your opponent screws up. When your opponent puts himself/herself in a vulnerable position, you should really know how to rush in and perform a high-damage, punishing combo. Make sure you can execute those combos well or you might end up getting punished yourself.
After that, study some mix-ups. You don’t want to be doing the same routine, rushing in and doing the exact same thing over and over, so learn some mix-ups to trick your opponent and mess with his/her head.
Lastly, study match-ups. There is no universal strategy in defeating all characters, so you’ll have to learn what normals, specials, combos, etc. are effective against the specific character you are fighting.
For fun… or anger and stress, try challenge mode trials. They make up these ridiculously hard combos that are not practical to use in a real match at all, but it can discipline you to get use to very difficult links, such as 1 or 2-frame links. If you can start doing 1-frame links pretty decently, more lenient combos will become a lot easier for you. It’s not for everyone, but I found challenge mode a little bit useful in that sense.
Finally, you could watch some pros play and try mimicking their style. Try to understand what they’re doing and why they’re doing it.
Overall, I would be spending the majority of the time perfecting the execution of bread and butter combos in training mode while you are waiting to get Live.